Sum theorems for maximally monotone operators of type (FPV)

The most important open problem in monotone operator theory concerns the maximal monotonicity of the sum of two maximally monotone operators provided that the classical Rockafellar’s constraint qualification holds. In this paper, we establish the maximal monotonicity of <i>A + B</i> provided that <i>A</i> and <i>B</i> are maximally monotone operators such that star(dom <i>A</i>) ∩ int dom <i>B</i> ≠ ∅, and <i>A</i> is of type (FPV). We show that when also dom <i>A</i> is convex, the sum operator <i>A + B</i> is also of type (FPV). Our result generalizes and unifies several recent sum theorems